Spikes or no spikes, I think you're entering the realm of needing dedicated resources, be it a VPS or small dedicated server, at least with your current resource usage. If you can cut it down, you might be able to get by.
I'm not willing to sponsor you, as you are running a business, should be making money, and accordingly should have no problem being able to pay for hosting. That said, I'm willing to host you (for free) for a month to at least get your site up again while you look for a permanent solution. We do run CloudLinux and a host of other abuse-prevention measures, so keep in mind that your site is going to slow to a crawl or start throwing errors when your resource usage goes through the roof, but it shouldn't be suspended.
I'm not willing to sponsor you, as you are running a business, should be making money, and accordingly should have no problem being able to pay for hosting. That said, I'm willing to host you (for free) for a month to at least get your site up again while you look for a permanent solution. We do run CloudLinux and a host of other abuse-prevention measures, so keep in mind that your site is going to slow to a crawl or start throwing errors when your resource usage goes through the roof, but it shouldn't be suspended.